It Starts with a Paradox

Part 2 of World Build­ing for Sci­ence Fiction

Part 2—It starts with a paradox

Pho­to by Rakice­vic Nenad from Pex­els

The Fer­mi para­dox tries to answer: Where are they (the aliens)? It looks at how fast trav­el is across the galaxy.  It says by infer­ence the time to explore the 100 bil­lion solar sys­tems with­in the galaxy. The para­dox assumes that the first civ­i­liza­tion to emerge will find itself alone the cos­mos.  Because they find them­selves alone, the civ­i­liza­tion will try to fig­ure out the answer to the ques­tion: Where are they?  This arti­cle will show pos­si­ble for a civ­i­liza­tion to answer this question.

First off, we show that this ques­tion is not an unrea­son­able one.  Using the laws of nature, a civ­i­liza­tion real­izes that anoth­er sci­en­tif­i­cal­ly advanced civ­i­liza­tion could exist else­where.  They’ll real­ize their star is one of 100 bil­lion with­in the galaxy.  They’ll build tele­scopes and dis­cov­er oth­er plan­ets orbit­ing those stars.  They’ll con­tem­plate life on those plan­ets and won­der about intel­li­gent life.  The first civ­i­liza­tion to emerge will lis­ten to the cos­mos.  Fail­ing to detect anoth­er civ­i­liza­tion, they’ll ques­tion their assump­tions. Even­tu­al­ly, they will ask and answer it.

To car­ry out the answer, the civ­i­liza­tion needs to explore every solar sys­tem in the galaxy.  Can this be done?  One solu­tion is by col­o­niz­ing every solar sys­tem and prepar­ing to explore as they move out­ward.  The home world sends out col­o­niz­er space­ships to two near­by solar sys­tems. Each of the col­o­niz­ers estab­lish­es a colony to build col­o­niz­ers that explore two more solar sys­tems and so forth.  If it takes 10 years to make the jour­ney and two gen­er­a­tions before the next col­o­niz­ers are ready, then the dou­bling time for explored sys­tems is 50 years.  So, 50 years at a pace, the num­ber of ships explor­ing dou­bles, and fifty years at a time, the num­ber of sys­tems dou­bles.  If the galaxy were spher­i­cal with the civilization’s home world at the cen­ter of the sphere, the dou­bling pro­ceeds for 1850 years until they explore 100 bil­lion suns.  Since the galaxy is not spher­i­cal, we must account for the size and shape of the galaxy in the calculations.

The diam­e­ter of our galaxy’s disk is over 100,000 light years. The light cross­ing time is 100,000 years.  If a rea­son­able largest speed (using Einstein’s spe­cial rel­a­tiv­i­ty) is half the speed of light, then the space­ship takes 200,000 years to cross it.  Using the fifty-year delay to set up the next colony, the cross­ing time is about two mil­lion years.  If civ­i­liza­tions last hun­dreds of mil­lions of years, two mil­lion years seems less than daunting.

An impor­tant con­sid­er­a­tion of this idea is look­ing at the escape speed of a solar mass star.  The escape speed is the speed leav­ing the solar sys­tem deter­mined from Newton’s uni­ver­sal law of grav­i­ty.  That speed for our sun is 42.1 kilo­me­ters per sec­ond (km/s).  Let’s use that speed to trav­el a light year or 6 tril­lion kilo­me­ters (that is 6 with 12 zeros or 6x10¹² km).  We find it takes nine thou­sand years to trav­el that distance.

A space­craft leav­ing at the escape speed of the sun will take longer than human civ­i­liza­tion has exist­ed to trav­el the dis­tance.  Scal­ing up to the size of the galaxy makes the jour­ney across the galaxy at 900 mil­lion years. With the uni­verse being 13.5 bil­lion years old, 900 mil­lion years is short.  Even the Earth, at 4.5 bil­lion years old, is old­er than the time it takes an object to cross the galaxy at 42.1 km/s—such a speed means it can hap­pen over four and a half times over the cur­rent age of the Earth.

We will con­sid­er the trav­el times com­put­ed in the last para­graph with great inter­est when we exam­ine pansper­mia in a future arti­cle.  We real­ize that a long lived (bil­lion-year plus) civ­i­liza­tion will cross the galaxy at an eas­i­ly attain­able speed.  The key point of the Fer­mi para­dox is that thor­ough­ly explor­ing a galaxy is doable in enough time.
As an emerg­ing civ­i­liza­tion, human­i­ty has sent probes on inter­stel­lar jour­neys (e.g. Voyager’s 1 and 2).  Humanity’s largest speeds are on order of 42 km/s, slow­er than the 300 thou­sand km/s of the speed of light.  Going faster makes the journey’s short­er.  And short­er dis­tances make the explo­ration of the galaxy eas­i­er.  So, we can con­tem­plate our even­tu­al explo­ration of the galaxy.  If we con­tem­plate it, why could not anoth­er alien civ­i­liza­tion con­tem­plate it?  If they could con­tem­plate it, why is there no evi­dence?  Hence, this is Fermi’s para­dox.  The first civ­i­liza­tion might ask: Are we alone?

A recent tele­vi­sion sci­ence fic­tion series revolved around a space­ship strand­ed on the far side of the galaxy after acci­den­tal­ly trav­el­ing through a worm­hole.  The space­ship esti­mat­ed that their jour­ney time back home to take sev­en­ty years—an aver­age speed of 1,429 times the speed of light.  The series last­ed sev­en years for them to return home—an aver­age speed of 14,290 times the speed of light.

We can con­tin­ue with the sci­ence fic­tion exam­ple. We need to deter­mine the time to explore all the solar sys­tems in the galaxy using their tech­nol­o­gy. We first assume a neg­li­gi­ble time to explore a solar sys­tem and the aver­age star sep­a­ra­tion of 4 light years. The jour­ney will explore twen­ty-five thou­sand solar sys­tems. They cross the entire breadth of the galaxy. Explor­ing four hun­dred-bil­lion solar sys­tems requires six­teen mil­lion ves­sels to com­plete the task.

To dou­ble the num­ber of space­ships, to reach 100 bil­lion requires you to dou­ble the num­ber thir­ty-sev­en times.  But the num­ber of dou­bling to reach 16 mil­lion is twen­ty-four.  Now it becomes a mat­ter of how rapid the dou­bling takes place. In our orig­i­nal exam­ple at half the speed of light and a fifty-year dou­bling time, it takes 1850 years to dou­ble to 100 bil­lion, or 1200 years to dou­ble to 16 mil­lion. The con­clu­sion for cal­cu­lat­ing the dou­bling times is to show that some­times, such as the half the speed of light, the speed of trav­el is lim­it­ing.  But, with the super­lu­mi­nal speeds, the abil­i­ty to build inter­stel­lar space­ships (AKA the dou­bling time) is limiting.

The main take-away from this arti­cle is that a civ­i­liza­tion capa­ble of a jour­ney to the stars can vis­it every solar sys­tem in the galaxy in a short time com­pared with cos­mic time scales.  A rea­son­able con­clu­sion based on the size of the galaxy; some civ­i­liza­tion would have made this effort.  The para­dox is why we haven’t found the evi­dence for that occurring—and if we cre­ate a sci­ence fic­tion uni­verse, what is the evidence?

As a sci­ence fic­tion world builder, the first deci­sion is how fast can a space­ship cross the galaxy.  This amounts to mak­ing a hard choice.  Is faster than light trav­el pos­si­ble?  Once we know the largest speed, we find the time it takes a civ­i­liza­tion to explore the galaxy com­plete­ly. There are more con­sid­er­a­tions beyond these, but they will wait for future articles.

In future arti­cles, we will revis­it the Fer­mi para­dox.  We’ll try to esti­mate the expan­sion rate of a civ­i­liza­tion across the galaxy and what this will mean if mul­ti­ple civ­i­liza­tions exist. We’ll exam­ine at the Fer­mi para­dox as it applies to pansper­mia.  Next time, we’ll look at the lev­els of civ­i­liza­tions based upon their tech­nol­o­gy.  We know it as the Kar­da­shev scale.